Curriculum / Math / 7th Grade / Unit 6: Geometry / Lesson 2
Math
Unit 6
7th Grade
Lesson 2 of 21
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Use vertical, complementary, and supplementary angle relationships to find missing angles.
The core standards covered in this lesson
7.G.B.5 — Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
The foundational standards covered in this lesson
4.MD.C.5 — Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
4.MD.C.6 — Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
4.MD.C.7 — Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
In small groups, with a ruler, draw two intersecting lines on a piece of paper.
Vertical angles are a pair of angles formed across from one another when two lines intersect. Based on the data from your class, what can you conclude about the measurements of vertical angles?
In the diagram below, line $${CD}$$ intersects line $${AB}$$ through point $$E$$. Ray $$EF$$ extends from point $$E$$.
Callie says that $$\angle CEB$$ is vertical to $$\angle AEF$$. Explain why her reasoning is incorrect and name the angle that is vertical to $$\angle CEB$$.
Three lines meet at a point, as shown below.
a. Describe the angle relationships you see in the diagram.
b. Set up and solve an equation to find the value of $$z$$.
Grade 7 Mathematics > Module 6 > Topic A > Lesson 2 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
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Three lines intersect at a common point, as shown in the diagram below.
Write and solve an equation to determine the value of $$x$$.
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Lesson 1
Lesson 3
Topic A: Angle Relationships
Identify and determine values of angles in complementary and supplementary relationships.
7.G.B.5
Use equations to solve for unknown angles. (Part 1)
Use equations to solve for unknown angles. (Part 2)
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Topic B: Circles
Define circle and identify the measurements radius, diameter, and circumference.
7.G.B.4
Determine the relationship between the circumference and diameter of a circle and use it to solve problems.
Solve real-world and mathematical problems using the relationship between the circumference of a circle and its diameter.
Determine the relationship between the area and radius of a circle and use it to solve problems.
Solve real-world and mathematical problems using the relationship between the area of a circle and its radius.
Solve problems involving area and circumference of two-dimensional figures (Part 1).
7.G.B.4 7.G.B.6
Solve problems involving area and circumference of two-dimensional figures (Part 2).
Topic C: Building Polygons and Triangles
Draw two-dimensional geometric shapes using rulers, protractors, and compasses.
7.G.A.2 7.G.B.5
Determine if three side lengths will create a unique triangle or no triangle.
7.G.A.2
Identify unique and identical triangles.
Determine if conditions describe a unique triangle, no triangle, or more than one triangle.
Topic D: Solid Figures
Identify and describe two-dimensional figures that result from slicing three-dimensional figures.
7.G.A.3
Find the surface area of right prisms.
7.G.B.6
Find the surface area of right pyramids.
Find the volume of right prisms and pyramids.
Solve real-world and mathematical problems involving volume.
Distinguish between and solve real-world problems involving volume and surface area.
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